Shut down Ubuntu and DO NOT boot from the hard disk or save anything to disk again until after recovering your files.
Boot the Ubuntu CD and use Software Center to install the Photorec utility.
Hit Control-Alt-T to open a terminal and run this command:
Insert a USB hard disk, it will be mounted in the filesystem under the path /media/Ubuntu
Use Photorec to recover the files from your hard disk and put them onto the USB hard disk.
You really need to be less gung-ho about installing a new OS - it seems you may have chosen the "erase entire disk" option. Also, even though partitioning is supposedly non-destructive these days, you should always back up to a different disk before modifying the partition layout of your disk. Backing up is tedious, losing irreplaceable data is a hundred times worse.
I try to treat the cause, not the symptom. I avoid the terminal in instructions, unless it's easier or necessary. My instructions will work within the Ubuntu system, instead of breaking or subverting it. Those are the three guarantees to the helpee.